Minimal Riesz energy on the sphere for axis-supported external fields
We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere Sd in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials |x−y|−s with d−2 s < d. For a given ax...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Report |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Brauchart, J.S. Dragnev, P.D. Saff, E.B. |
| description | We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere Sd in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials |x−y|−s with d−2 s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on Sd is determined. The special case s = d − 2 yields interesting phenomena, which we investigate in detail. A weak∗ asymptotic analysis is provided as s ! (d − 2)+. |
| doi_str_mv | 10.34657/2671 |
| format | Report |
| fullrecord | <record><control><sourceid>datacite_PQ8</sourceid><recordid>TN_cdi_datacite_primary_10_34657_2671</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_34657_2671</sourcerecordid><originalsourceid>FETCH-datacite_primary_10_34657_26713</originalsourceid><addsrcrecordid>eNqNjrEOgjAURTtoIlH-oYsj2gItMhuMi4txb6o8pAmWpq8m4NeLxg9wOss9uYeQmLNNlktRbFNZ8BmJ-E7mSSFKuSAxorkylqVpKYSMSHUy1jx0R88G8EXBgr-PtLc0tEDRteCBNr2nejCY4NO53geoKQwBvJ20xkBX44rMG90hxD8uyfpQXfbHpNZB30wA5fz04kfFmfqmqU9a9u_uDbBHPpw</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>report</recordtype></control><display><type>report</type><title>Minimal Riesz energy on the sphere for axis-supported external fields</title><source>DataCite</source><creator>Brauchart, J.S. ; Dragnev, P.D. ; Saff, E.B.</creator><creatorcontrib>Brauchart, J.S. ; Dragnev, P.D. ; Saff, E.B.</creatorcontrib><description>We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere Sd in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials |x−y|−s with d−2 s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on Sd is determined. The special case s = d − 2 yields interesting phenomena, which we investigate in detail. A weak∗ asymptotic analysis is provided as s ! (d − 2)+.</description><identifier>ISSN: 1864-7596</identifier><identifier>DOI: 10.34657/2671</identifier><language>eng</language><publisher>Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach</publisher><subject>Balayage ; Equilibrium Measures ; Extremal Measures ; Minimum Energy ; Riesz kernel ; Weighted Energy</subject><creationdate>2009</creationdate><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>776,780,1888,4476,27902</link.rule.ids><linktorsrc>$$Uhttps://commons.datacite.org/doi.org/10.34657/2671$$EView_record_in_DataCite.org$$FView_record_in_$$GDataCite.org</linktorsrc></links><search><creatorcontrib>Brauchart, J.S.</creatorcontrib><creatorcontrib>Dragnev, P.D.</creatorcontrib><creatorcontrib>Saff, E.B.</creatorcontrib><title>Minimal Riesz energy on the sphere for axis-supported external fields</title><description>We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere Sd in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials |x−y|−s with d−2 s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on Sd is determined. The special case s = d − 2 yields interesting phenomena, which we investigate in detail. A weak∗ asymptotic analysis is provided as s ! (d − 2)+.</description><subject>Balayage</subject><subject>Equilibrium Measures</subject><subject>Extremal Measures</subject><subject>Minimum Energy</subject><subject>Riesz kernel</subject><subject>Weighted Energy</subject><issn>1864-7596</issn><fulltext>true</fulltext><rsrctype>report</rsrctype><creationdate>2009</creationdate><recordtype>report</recordtype><sourceid>PQ8</sourceid><recordid>eNqNjrEOgjAURTtoIlH-oYsj2gItMhuMi4txb6o8pAmWpq8m4NeLxg9wOss9uYeQmLNNlktRbFNZ8BmJ-E7mSSFKuSAxorkylqVpKYSMSHUy1jx0R88G8EXBgr-PtLc0tEDRteCBNr2nejCY4NO53geoKQwBvJ20xkBX44rMG90hxD8uyfpQXfbHpNZB30wA5fz04kfFmfqmqU9a9u_uDbBHPpw</recordid><startdate>2009</startdate><enddate>2009</enddate><creator>Brauchart, J.S.</creator><creator>Dragnev, P.D.</creator><creator>Saff, E.B.</creator><general>Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach</general><scope>PQ8</scope></search><sort><creationdate>2009</creationdate><title>Minimal Riesz energy on the sphere for axis-supported external fields</title><author>Brauchart, J.S. ; Dragnev, P.D. ; Saff, E.B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-datacite_primary_10_34657_26713</frbrgroupid><rsrctype>reports</rsrctype><prefilter>reports</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Balayage</topic><topic>Equilibrium Measures</topic><topic>Extremal Measures</topic><topic>Minimum Energy</topic><topic>Riesz kernel</topic><topic>Weighted Energy</topic><toplevel>online_resources</toplevel><creatorcontrib>Brauchart, J.S.</creatorcontrib><creatorcontrib>Dragnev, P.D.</creatorcontrib><creatorcontrib>Saff, E.B.</creatorcontrib><collection>DataCite</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Brauchart, J.S.</au><au>Dragnev, P.D.</au><au>Saff, E.B.</au><format>book</format><genre>unknown</genre><ristype>RPRT</ristype><btitle>Minimal Riesz energy on the sphere for axis-supported external fields</btitle><date>2009</date><risdate>2009</risdate><issn>1864-7596</issn><abstract>We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere Sd in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials |x−y|−s with d−2 s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on Sd is determined. The special case s = d − 2 yields interesting phenomena, which we investigate in detail. A weak∗ asymptotic analysis is provided as s ! (d − 2)+.</abstract><pub>Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach</pub><doi>10.34657/2671</doi></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 1864-7596 |
| ispartof | |
| issn | 1864-7596 |
| language | eng |
| recordid | cdi_datacite_primary_10_34657_2671 |
| source | DataCite |
| subjects | Balayage Equilibrium Measures Extremal Measures Minimum Energy Riesz kernel Weighted Energy |
| title | Minimal Riesz energy on the sphere for axis-supported external fields |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-10T23%3A04%3A12IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-datacite_PQ8&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=unknown&rft.btitle=Minimal%20Riesz%20energy%20on%20the%20sphere%20for%20axis-supported%20external%20fields&rft.au=Brauchart,%20J.S.&rft.date=2009&rft.issn=1864-7596&rft_id=info:doi/10.34657/2671&rft_dat=%3Cdatacite_PQ8%3E10_34657_2671%3C/datacite_PQ8%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |